Essential Practice Questions: Quadratic Equation Questions for IPMAT 2025

Overview: Mastering quadratic equation questions is necessary to crack the exam with excellent scores. This article provides important quadratic equation questions for IPMAT 2025 to help you practice. Read on to enhance your problem-solving skills and ace the exam!

In most entrance exams, you'll encounter a mathematics section that includes questions from various concepts, with the quadratic equation being one of the essential topics.

Although quadratic equations might seem complex at first glance, they can be solved quickly and efficiently using the correct formulas and methods.

This post will guide you through essential quadratic equation questions for the IPMAT entrance exam, providing several examples, solutions, and practice papers to help you master this topic.

Download Free Study Materials for IPMAT 2025 by SuperGrads

What are Quadratic Equations? 

Quadratic equations are a type of equation in algebra that can be rearranged in standard form as ax^{2}+bx+c=0 where x represents as unknown, and a, b, and c represent known numbers, and a ≠ 0.

If a = 0, the equation is linear, not quadratic, as there is no ax^2 term.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

• 6x² + 11x - 35 = 0
• x² -x - 3 = 0
• 2x² - 4x - 2 = 0
• -4x² - 7x +12 = 0
• 5x² - 2x - 9 = 0
• 20x² -15x - 10 = 0

Quadratic Equation Questions for IPMAT with Answers

Here is the list of questions curated from previous year's IPMAT Question Papers.

The subject mentor from Supergrads has solved the questions below with a detailed explanation. 

Solve these quadratic equations and enhance your preparation for the upcoming IPMAT exam.

Q1. If 𝛼 ≠ 𝛽 but α ² = 5α − 3 and β ² = 5β − 3 then the equation whose roots are 𝛼/𝛽 and 𝛽/𝛼 is

• (a) 3x ² − 25x +3 = 0
• (b) x ² + 5𝑥 −3 = 0
• (c) x ² − 5𝑥 +3 = 0
• (d) 3𝑥 ² − 19𝑥 + 3 = 0

Answer: D

Q2. Difference between the corresponding roots of x ² + ax+ b = 0 and x ² + bx + 𝑎 = 0 is same and 𝑎 ≠ 𝑏, then

• (a) 𝑎 + 𝑏 + 4 = 0
• (b) 𝑎 + 𝑏 − 4 = 0
• (c) 𝑎 − 𝑏 − 4 = 0
• (d) 𝑎 − 𝑏 + 4 = 0

Answer: A

Q3. If p and q are the roots of the equation x² + px + q = 0 then

• (a) 𝑝 = 1, 𝑞 = −2
• (b) 𝑝 = 0, 𝑞 = 1
• (c) 𝑝 = −2, 𝑞 = 0
• (d) 𝑝 = −2, 𝑞 = 1

Answer: A

Q4. If a , b , c are distinct positive real numbers and a² + b ² + c ² = 1 then 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 is

• (a) less than 1
• (b) equal to 1
• (c) greater than 1
• (d) any real no

Answer: A

Q5. The value of a for which one root of the quadratic equation (a² 2 − 5a+ 3)x ²2 + (3a − 1)x + 2 = 0 is twice as large as the other is

• (a) -2/3
• (b) 1/3
• (c) -1/3
• (d) 2/3

Answer: D

Q6. If the sum of the roots of the quadratic equation ax² +bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in 

• (a) geometric progression
• (b) harmonic progression
• (c) arithmetic-geometric progression
• (d) arithmetic progression

Answer: B

Q7. Let two numbers have an arithmetic mean nine and geometric mean 4 . Then these numbers are the roots of the quadratic equation

• (a) x ² + 18𝑥 −16 = 0
• (b) x ² − 18𝑥 +16 = 0
• (c) x ² + 18𝑥 +16 = 0
• (d) x ² − 18𝑥 −16 = 0

Answer: B

Q8. If (1 −𝑝) is a root of quadratic equation x² + 𝑝𝑥 +(1 −𝑝) = 0 then its roots are

• (a) 0, -1
• (b) -1, 1
• (c) 0, 1
• (d) -1, 2

Answer: D

Q9. If one root of the equation x²+ 𝑝𝑥 + 12 = 0 is 4 while the equation x ² + 𝑝𝑥 + 𝑞 = 0 has equal roots, then the value of q is

• (a) 3
• (b) 12
• (c) 49/4
• (d) 4

Answer: C

Q10.  If the roots of the equation x² −𝑏𝑥 + 𝑐 = 0 be two consecutive integers, then b ² −4𝑐 equals

• (a) 3
• (b) -2
• (c) 1
• (d) 2

Answer: C

Mastering quadratic equations is essential for cracking the IPMAT exam. Regular practice with various types of quadratic equation questions can significantly enhance your problem-solving skills and boost your confidence.

Quadratic Equation Questions for IPMAT 2025 with Explanations

Question 1

Solve the quadratic equation: x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0.

Click to Attempt Free Mock Test for IPMAT Prep

Question 2

Solve the quadratic equation: 2x2+3x−2=02x^2 + 3x - 2 = 02x2+3x−2=0.

Question 3

Find the roots of the quadratic equation: x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0.

Question 4

Solve the quadratic equation: x2−2x−8=0x^2 - 2x - 8 = 0x2−2x−8=0.

Question 5

Solve the quadratic equation: 3x2+7x+2=03x^2 + 7x + 2 = 03x2+7x+2=0.

Unlock Grandmaster’s Box for IPMAT 2025 from SuperGrads

IPMAT Quadratic Equation Questions with Answers PDF

For more quadraticeEquation questions, download the quadratic equation questions for IPMAT pdf, which includes questions and solutions.

Enhance your preparation for IPMAT by solving these Quadratic Equation Questions for IPMAT and score good marks in the mathematics section.

How to Solve IPMAT Quadratic Equation Questions for IPMAT?

You can solve the below questions using various methods; one such is by factorization. 

1. Put all the terms on one side of the equal sign, leaving zero on the other side. 
2. Do the factorization.
3. Set each factor equal to zero.
4. Solve each of these equations.
5. Check your solution by inserting your answer into the original equation.

Important Formulas to Solve Quadratic Equation Questions for IPMAT

Here is the list of formulas that you can use to solve IPMAT Questions. 

• The standard form of a quadratic equation is ax² + bx + c = 0
• The discriminant of the quadratic equation is D = b² - 4ac
• For D > 0 the roots are real and distinct.
• For D = 0 the roots are real and equal.
• For D < 0 the roots do not exist, or the roots are imaginary.
• The formula to find the roots of the quadratic equation is x = 
• The sum of the roots of a quadratic equation is α + β = -b/a = - Coefficient of x/ Coefficient of x².
• The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x²
• The quadratic equation having roots α, β, is x² - (α + β)x + αβ = 0.
• For positive values of a (a > 0), the quadratic expression f(x) = ax² + bx + c has a minimum value at x = -b/2a.
• For negative value of a (a < 0), the quadratic expression f(x) = ax² + bx + c has a maximum value at x = -b/2a.
• For a > 0, the range of the quadratic equation ax² + bx + c = 0 is [b² - 4ac/4a, ∞)
• For a < 0, the range of the quadratic equation ax² + bx + c = 0 is : (∞, -(b² - 4ac)/4a]

Prepare with Online Lectures for IPMAT 2025 by SuperGrads

Preparation Strategy for IPMAT Quadratic Equation Questions

Understanding the Importance

Mastering quadratic equation questions is essential to excel in the IPMAT exam. Quadratic equations, though initially appearing complex, can be solved efficiently with the right approach. This section will guide you through an effective preparation strategy, incorporating important concepts, formulas, and problem-solving techniques to help you ace the quadratic equation questions in the IPMAT exam.

Key Concepts and Formulas

Before diving into practice, ensure you understand the fundamental concepts and formulas related to quadratic equations:

1. Standard Form: A quadratic equation is generally written as ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where xxx is the variable, and a,b,a, b,a,b, and ccc are constants with a≠0a \neq 0a=0.

2. Discriminant: The discriminant (DDD) of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 is given by D=b2−4acD = b^2 - 4acD=b2−4ac. The discriminant determines the nature of the roots:

• D>0D > 0D>0: Two distinct real roots
• D=0D = 0D=0: Two equal real roots
• D<0D < 0D<0: No real roots (roots are complex)

3. Roots Formula: The roots of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 can be found using the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

4. Sum and Product of Roots:

• Sum of the roots (α+β\alpha + \betaα+β): −ba-\frac{b}{a}−ab​
• Product of the roots (αβ\alpha \betaαβ): ca\frac{c}{a}ac​

Problem-Solving Techniques

To solve quadratic equation questions effectively, use these methods:

Factorization:

• Rewrite the equation in the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0.
• Find two numbers that multiply to acacac and add up to bbb.
• Factorize and solve for xxx.

Completing the Square:

• Rewrite the equation in the form ax2+bx=−cax^2 + bx = -cax2+bx=−c.
• Add and subtract (b2a)2\left( \frac{b}{2a} \right)^2(2ab​)2 on both sides.
• Solve for xxx after simplifying.

Using the Quadratic Formula:

• Directly apply the quadratic formula to find the roots.

Practice Regularly

Consistent practice is crucial for mastering quadratic equations. Work on various types of questions, including those involving:

• Basic factorization
• Special cases with real, equal, and complex roots
• Application of the quadratic formula

Example Problems

Here are a few example problems to get you started:

1. Solve: x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0

• Factorize to (x−2)(x−3)=0(x - 2)(x - 3) = 0(x−2)(x−3)=0
• Roots: x=2x = 2x=2 and x=3x = 3x=3

2. Solve: 2x2+3x−2=02x^2 + 3x - 2 = 02x2+3x−2=0

• Using the quadratic formula: x=−3±9+164x = \frac{-3 \pm \sqrt{9 + 16}}{4}x=4−3±9+16​​
• Roots: x=12x = \frac{1}{2}x=21​ and x=−2x = -2x=−2

3. Solve: x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0

• Completing the square: (x+2)2=0(x + 2)^2 = 0(x+2)2=0
• Root: x=−2x = -2x=−2

Time Management

Practice solving quadratic equations within a time limit to improve speed and accuracy. Allocate specific times for each problem and gradually reduce the time as you become more proficient.

Mock Tests and Revision

Incorporate quadratic equation questions into your mock tests to simulate exam conditions. Regular revision of key concepts and formulas will reinforce your understanding and boost your confidence.

Mastering quadratic equations is crucial for excelling in the IPMAT exam. By understanding fundamental concepts, practicing various problem-solving techniques, and regularly revising key formulas, you can significantly enhance your mathematical abilities.

Free Demo Classes to Prepare for IPMAT 2025 Exam

Key Takeaways:

• Essential Concepts: Understand the standard form of quadratic equations, the discriminant, and the quadratic formula to solve various types of problems.
• Problem-Solving Techniques: Use factorization, completing the square, and the quadratic formula to solve quadratic equations efficiently.
• Regular Practice: Consistent practice with diverse types of quadratic equation questions is crucial for improving problem-solving skills and speed.
• Time Management: Practice solving questions within a time limit to enhance speed and accuracy during the exam.
• Mock Tests and Revision: Incorporate quadratic equation questions in mock tests and regularly revise key concepts and formulas to reinforce understanding and boost confidence.